Estimate the interest rate and minimize risk, Macroeconomics

1. In December 1979 it was possible to buy a January 1980 contract in gold at the New York Commodity Exchange for $487.50 per ounce and sell an October 1981 contract for $614.80 on the same day. Under what condition would this have been profitable? Exactly what could you have done to make arbitrage profit if you had taken these possible? What type of interest rate is relevant in this context?

2. Assume that the risk free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 78 and the futures price for a contract deliverable in four months is 80. What arbitrage opportunities does this create?

3. Regression analysis is one technique often used in studying hedging problems. Using daily data for the previous year, a regression of KOSPI200 cash index returns on near KOSPI 200 futures returns yields the following output:

RC = α + βRf + ε

? = 0.00050, β = 0.82, R2 = 0.90, σ (ε) = 0.00217

Suppose that you wish to hedge 1-day risk of a $17M KOSPI200 index stock basket. If the current KOSPI200 cash index equals 265, how many near KOSPI200 futures 2 contracts should be sold to minimize risk?